Human behaviour in various circumstances mirrors the corresponding brain connectivity patterns, which are suitably represented by functional brain networks. While the objective analysis of these networks by graph theory tools deepened our understanding of brain functions, the multi-brain structures and connections underlying human social behaviour remain largely unexplored. In this study, we analyse the aggregate graph that maps coordination of EEG signals previously recorded during spoken communications in two groups of six listeners and two speakers. Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. Our results reveal that the topological quantifiers provide new suitable measures for differences in the brain activity patterns and inter-brain synchronisation between speakers and listeners. Moreover, the higher topological complexity correlates with the listener&rsquo;s concentration to the story, confirmed by self-rating, and closeness to the speaker&rsquo;s brain activity pattern, which is measured by network-to-network distance. The connectivity structures of the frontal and parietal lobe consistently constitute distinct clusters, which extend across the listener&rsquo;s group. Formally, the topology quantifiers of the multi-brain communities exceed the sum of those of the participating individuals and also reflect the listener&rsquo;s rated attributes of the speaker and the narrated subject. In the broader context, the presented study exposes the relevance of higher topological structures (besides standard graph measures) for characterising functional brain networks under different stimuli.

pone.0166787.g010: Structure of inter-brain linking.Superbrain network of the speaker S2 and the listener L2−3, illustrating proper coordination, (left), and a weakly connected two-brain structure of the listener L1−4 and the speaker S1, corresponding to wrong coordination (right). Different colour of nodes indicates the identified functional communities. The node’s labels belong to the unique list of 882 scalp locations of all participants; for example, L2−3−TP9 and S2−F7 indicate the channel “TP9” on the scalp of the listener 3 in group 2, and channel “F7” of the scalp of the speaker S2, respectively. See also the overlaps in Fig 6 and distances in Fig 8 for these pairs.

Mentions:
Apart from the diagonal blocks of the adjacency matrix in Fig 3, the off-diagonal matrices exhibiting the inter-brain connections provide valuable information about the communication impact (speaker–listeners) as well as the brain-function synchronisation under the same input stimulus (listener–listener correlations). These connections contribute to a nontrivial structure of the multi-brain network. In Fig 10, we show two representative examples visualising differences in two-brain networks of a listener and a speaker. In one case, L2−3 well correlates with the speaker S2. The corresponding two-brain network has 630 cross-links and an original structure with two communities, each of which contains the scalp locations of both individuals. This super-brain structure confirms a real focus of the listener L2−3 to the speaker’s S2 story, in full agreement with the corresponding distance and SBN overlap measures for L2−3 and S2 discussed above, as well as the listener’s self-reported experience in Table A in S1 File. Oppositely, the two-brain network of the listener L1−4 and the speaker S1 exhibits very few cross-links (57) and a community structure featuring separate brains. These results also agree well with the self-reported low concentration, uninteresting and confusing story, and bad qualities of the speaker (see Table A in S1 File).

pone.0166787.g010: Structure of inter-brain linking.Superbrain network of the speaker S2 and the listener L2−3, illustrating proper coordination, (left), and a weakly connected two-brain structure of the listener L1−4 and the speaker S1, corresponding to wrong coordination (right). Different colour of nodes indicates the identified functional communities. The node’s labels belong to the unique list of 882 scalp locations of all participants; for example, L2−3−TP9 and S2−F7 indicate the channel “TP9” on the scalp of the listener 3 in group 2, and channel “F7” of the scalp of the speaker S2, respectively. See also the overlaps in Fig 6 and distances in Fig 8 for these pairs.

Mentions:
Apart from the diagonal blocks of the adjacency matrix in Fig 3, the off-diagonal matrices exhibiting the inter-brain connections provide valuable information about the communication impact (speaker–listeners) as well as the brain-function synchronisation under the same input stimulus (listener–listener correlations). These connections contribute to a nontrivial structure of the multi-brain network. In Fig 10, we show two representative examples visualising differences in two-brain networks of a listener and a speaker. In one case, L2−3 well correlates with the speaker S2. The corresponding two-brain network has 630 cross-links and an original structure with two communities, each of which contains the scalp locations of both individuals. This super-brain structure confirms a real focus of the listener L2−3 to the speaker’s S2 story, in full agreement with the corresponding distance and SBN overlap measures for L2−3 and S2 discussed above, as well as the listener’s self-reported experience in Table A in S1 File. Oppositely, the two-brain network of the listener L1−4 and the speaker S1 exhibits very few cross-links (57) and a community structure featuring separate brains. These results also agree well with the self-reported low concentration, uninteresting and confusing story, and bad qualities of the speaker (see Table A in S1 File).

Human behaviour in various circumstances mirrors the corresponding brain connectivity patterns, which are suitably represented by functional brain networks. While the objective analysis of these networks by graph theory tools deepened our understanding of brain functions, the multi-brain structures and connections underlying human social behaviour remain largely unexplored. In this study, we analyse the aggregate graph that maps coordination of EEG signals previously recorded during spoken communications in two groups of six listeners and two speakers. Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. Our results reveal that the topological quantifiers provide new suitable measures for differences in the brain activity patterns and inter-brain synchronisation between speakers and listeners. Moreover, the higher topological complexity correlates with the listener&rsquo;s concentration to the story, confirmed by self-rating, and closeness to the speaker&rsquo;s brain activity pattern, which is measured by network-to-network distance. The connectivity structures of the frontal and parietal lobe consistently constitute distinct clusters, which extend across the listener&rsquo;s group. Formally, the topology quantifiers of the multi-brain communities exceed the sum of those of the participating individuals and also reflect the listener&rsquo;s rated attributes of the speaker and the narrated subject. In the broader context, the presented study exposes the relevance of higher topological structures (besides standard graph measures) for characterising functional brain networks under different stimuli.